The question is as follows:
Let's say that you play the lottery (when you are old enough). Six numbers without repetition are chosen from 1-40, If you pick all six numbers, you win \$1 million. If you pick five of the six, you win \$1000. If you pick four of the six, you win \$100. What is the expected value of a \$1 lottery ticket? Note: the way you play this lottery game if by receiving a card with an empty circle under each number from 1-40. You will fill in the circle underneath each of the six numbers you choose.
I have tried all sorts of work but they all result to either a ridiculously small answer or a ridiculously large answer, and the correct answer is -0.467. Can someone help me out here?
Best Answer
Expected payout is
$$1,000,000 \frac{{6\choose 6}{34\choose 0}}{40\choose 6} + 1000 \frac{{6\choose 5}{34\choose 1}}{40\choose 6}+100 \frac{{6\choose 4}{34\choose 2}}{40\choose 6},$$
which if your answer is correct should equal 0.533.